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If I have some predefined coordinate system — “my rest frame,” then I pick an “inertial frame” moving at some velocity with respect to my “rest frame.” Special relativity states that in the rest frame, the speed of an object can not exceed the speed of light — however I could pick any velocity for my inertial frame, say $99.9$% or even $200$% $c$, then say that my ship is traveling at $99.9$% $c$ in the inertial frame, and now I have a ship moving at $199.8$% or $299.9$% $c$ relative to the original rest frame?

Isn’t there some sort of self-contradiction here? Is the proposition that no object cannot exceed the speed of light simply a phenomenon resulting from observation assuming that time “runs” at the same rate for both observers, not from the motion of the actual object?

Qmechanic
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Joeseph123
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1 Answers1

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The postulates of special relativity are

  1. The laws of physics are the same in all inertial frames of reference.
  2. As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity $c$ that is independent of the state of motion of the emitting body.

The first postulate ensures that there is no preferred inertial frame of reference; all inertial frames are the same and the laws of physics are invariant.

The second one speaks about the invariance of $c$, the speed of light. In other words, the speed of light in free space has the same value in all inertial frames of reference.

...however I could pick any velocity for my inertial frame, say 99.9% or even 200% c...

By definition, you cannot choose an inertial reference frame which is moving at any arbitrary speed $> c$. It just does not exist.

Why does it not exist? Because the special relativity respects Lorentz transformation and not Galilean. Said in simpler words, the valid frames consist solely of those in which speed of light is precisely $c$, all of which are linked by Lorentz transformation.

If you still want to define a frame which is moving at $200\% c$, you cannot use this theory. However, keep in mind that special relativity has been far more successful when space-time curvature is flat. A surprisingly large number of papers, going all the way back to the birth of relativity, have been written by people trying to find a way to extend the Lorentz transformations to superluminal speeds, and these have all turned out to be failures [ref].

...then say that my ship is travelling at 99.9% c in the inertial frame, and now I have a ship moving at 199.8% or 299.9% c relative to the original rest frame?

Neither of them. You need to use Einstein's law for addition. For a ship moving at velocity $u'$ in the frame $S'$ and the velocity of inertial frame $S'$ w.r.t to another inertial frame $S$ is $v$, then someone in $S$ would observe the velocity of ship as $u$ given by $$u = {v+u'\over 1+(v u'/c^2)} < c$$

Galaxies moving faster than light requires General Relativity. For more about that, read this and this along with links therein.

PolaroidDreams
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